I'm a little drunk right now but I'm gonna try to figure this out for you, gimme like 5 hours.

are you sure it has an inverse? i ran it through an online calculator and says doesn't exist

To know if a square-matrix has an inverse, you should first calculate its determinant.

In your case, det A = 0.

A square-matrix has an inverse if and only if its determinant is an inversible element (ie : it's non-zero if you're working over R or C)..

This post was edited by feanur on Oct 28 2016 12:11am

R or C?

Answer:
(pseudoinverse)
How to: https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html
Calculate determinant.
Create matrix of minors.
Turn matrix of minors into matrix of cofactors.
Transpose matrix of cofactors into adjugate.
Multiply adjugate by determinant of original matrix.
Inverse of original matrix is left.

This post was edited by Dontrunaway on Oct 28 2016 07:35pm

i assume real and complex numbers

Yes.

As a counter-example, if you consider matrixes with integer coefficients, the condition to have an inverse turns to :
det A = 1 or det A = -1
(otherwise it could have an inverse with real coefficients, but not all of them would be integers).

so no inverse for that matrix